Have particles come from faces
When you are planning to make those kinds of particle systems, you should use a Hair system instead of an Emitter one.

In your system the particles are being thrown from the faces and, despite you have the system freezed at frame 0 (I think Blender don't use negative frames in any simulation), it looks like some particles had enough velocity to be outside of the faces.

So the best approach to achieve your work is using a Hair Particle System. It's very simple for your purpose:


Create a Particle System and set it to Hair. The Hair strands are perpendicular to the surface, just what you want.
Change the Number of particles. The Hair Length is not necessary for you.
Under the Render properties of the particle system, select object and then set Dupli Object to your tree. Then change the size at your will.
Maybe you need to re-orient your tree in Edit Mode to align the vertical axis.


Additionally, you can create a group of a few different trees and set the Render particles to Group. The particle system is going to randomly select the trees for every strand.

Regarding to your actual situation, maybe if you set the Normal Velocity to 0, those trees would not float. But the Hair System is the best choice in this case.